# CLEAN WORKSPACE AND LOAD PACKAGES --------------------------------------------

rm(list = ls())
library(datasim)
library(tidyverse)
## ── Attaching packages ────────────────────────────────── tidyverse 1.2.1 ──
## ✔ ggplot2 2.2.1.9000     ✔ purrr   0.2.4     
## ✔ tibble  1.4.2          ✔ dplyr   0.7.4     
## ✔ tidyr   0.8.0          ✔ stringr 1.3.0     
## ✔ readr   1.1.1          ✔ forcats 0.3.0
## ── Conflicts ───────────────────────────────────── tidyverse_conflicts() ──
## ✖ dplyr::filter() masks stats::filter()
## ✖ dplyr::lag()    masks stats::lag()
## ✖ dplyr::vars()   masks ggplot2::vars()
# SIMULATE MULTIVARIATE SPATIAL DATA -------------------------------------------

# set.seed(4)
Corr <- matrix(c(1, -0.3, 0, -0.3, 1, 0.3, 0, 0.3, 1), nrow = 3)
sigmas <- rep(0.4^0.5, 3)
D <- diag(sigmas)
Cov <- D %*% Corr %*% D

# beta <- c(-0.5, 0, 0.5)
beta <- c(0, 0, 0)
variance <- 0.6 * matrix(c(1, 0, 0, 0, 1, 0, 0, 0, 1), nrow = 3)
cor.model <- "exp_cor"
cor.params <- list(list(phi = 0.04), list(phi = 0.04), list(phi = 0.1))

f <- list(
  mean ~ mfe(x1, beta = get("beta")) +
    mre(factor(id), sigma = get("Cov")) +
    mgp(list(s1), variance = get("variance"), cor.model = get("cor.model"),
        cor.params = get("cor.params")),
  sd ~ I(0)
  )

n <- 300
m <- 3
(data_geo <- sim_model(formula = f, n = n, responses = m))
## # A tibble: 900 x 9
##       id      x1     s1 mre.factor.mean mgp.list.mean     mean    sd
##    <int>   <dbl>  <dbl>           <dbl>         <dbl>    <dbl> <dbl>
##  1     1  0.476  0.285        -0.185            0.904  0.719      0.
##  2     2 -0.856  0.729        -0.0733          -1.13  -1.20       0.
##  3     3 -1.84   0.0912        0.477           -0.354  0.123      0.
##  4     4  0.191  0.527         0.0108           1.18   1.19       0.
##  5     5  0.0108 0.240         0.329           -0.208  0.121      0.
##  6     6 -1.58   0.379        -0.251            0.252  0.00173    0.
##  7     7 -0.675  0.690        -0.0572           0.280  0.223      0.
##  8     8  1.07   0.621        -0.253           -0.977 -1.23       0.
##  9     9  0.483  0.811         0.000684        -0.276 -0.275      0.
## 10    10  1.11   0.682        -0.594            0.503 -0.0912     0.
## # ... with 890 more rows, and 2 more variables: response <dbl>,
## #   response_label <int>
# knitr::kable(head(data_model, 10))

X <- matrix(rnorm(20), 10, 2)

# VISUALIZE MULTIVARIATE SPATIAL DATA ------------------------------------------

ggplot(data_geo, aes(x1, response)) +
  geom_smooth(aes(col = factor(response_label))) +
  geom_point(aes(col = factor(response_label)))
## `geom_smooth()` using method = 'loess' and formula 'y ~ x'

ggplot(data_geo, aes(s1, mgp.list.mean)) +
  geom_line(aes(col = factor(response_label)))

data_geo %>%
  dplyr::select(id, mre.factor.mean, response_label) %>%
  spread(response_label, mre.factor.mean) %>%
  dplyr::select(-id) %>%
  GGally::ggpairs(aes(fill = "any"))

data_geo_wide <- data_geo %>%
  dplyr::rename(ability = response, id_person = id) %>%
  gather(var, value, mre.factor.mean:ability) %>%
  mutate(var = paste0(var, response_label)) %>%
  select(-response_label) %>%
  spread(var, value)


# SIMULATE ITEM FACTOR DATA ----------------------------------------------------

q <- 10
init_data <- purrr::map(1:q, ~ data_geo_wide) %>%
  purrr::reduce(rbind)

# n <- 300
difficulty <- matrix((1:q - 5)/10 * 2, nrow = 1)
discrimination1 <- seq(0.4, 1.5, length.out = q)
discrimination2 <- runif(q, 0, 2)
discrimination3 <- runif(q, 0, 2)
discrimination1[1] <- 1
discrimination1[c(3, 5, 8)] <- 0
discrimination2[1:2] <- c(0, 1)
discrimination2[c(4, 5, 10)] <- 0
# discrimination3[1:3] <- c(0, 0, 1)
# discrimination1 <- discrimination1 * 0.3
# discrimination2 <- discrimination2 * 0.3
cbind(discrimination1, discrimination2, discrimination3)
##       discrimination1 discrimination2 discrimination3
##  [1,]       1.0000000      0.00000000      0.03342079
##  [2,]       0.5222222      1.00000000      1.93959064
##  [3,]       0.0000000      1.80589290      1.54502217
##  [4,]       0.7666667      0.00000000      1.58316375
##  [5,]       0.0000000      0.00000000      0.13343296
##  [6,]       1.0111111      1.99441057      1.51071104
##  [7,]       1.1333333      0.77046483      1.04485630
##  [8,]       0.0000000      0.01718154      0.12162534
##  [9,]       1.3777778      0.86570335      1.98672634
## [10,]       1.5000000      0.00000000      0.80690463
f <- list(
  prob ~ mfa(ones, beta = get("difficulty")) +
    mfe(ability1, beta = get("discrimination1")) +
    mfe(ability2, beta = get("discrimination2")),
  # + mfe(ability3, beta = get("discrimination3")),
  size ~ I(1)
  )

data_long <- sim_model(formula = f,
                        link_inv = list(pnorm, identity),
                        generator = rbinom,
                        responses = q,
                        n = n,
                        init_data = init_data
                        )

data_long <- dplyr::rename(data_long, subject = id,
                           item = response_label, y = response)

# VISUALIZE ITEM FACTOR DATA ---------------------------------------------------

explor <- data_long %>%
  group_by(subject) %>%
  summarize(endorse = mean(y),
            ability1 = unique(ability1),
            ability2 = unique(ability2),
            # ability3 = unique(ability3),
            x1 = unique(x1))
ggplot(explor, aes(ability1, endorse)) + geom_point(alpha = 0.5)

ggplot(explor, aes(ability2, endorse)) + geom_point(alpha = 0.5)

# ggplot(explor, aes(ability3, endorse)) + geom_point(alpha = 0.5)
# ggplot(explor, aes(x1, endorse)) + geom_point(alpha = 0.5)

# PREPARE DATA -----------------------------------------------------------------

response <- data_long$y
dist <- as.matrix(dist(dplyr::select(data_geo_wide, s1)))
# dist <- as.matrix(dist(dplyr::select(data_geo_wide, s1)[order(data_geo_wide$s1),]))
# dist <- dist[order(data_geo_wide$s1),]
n
## [1] 300
q
## [1] 10
m <- 2
# iter <- 5 * 10 ^ 4
iter <- 5 * 10 ^ 2
cor.params <- c(0.04, 0.04)
sig.params <- c(0.6 ^ 0.5, 0.6 ^ 0.5)
fix.sigma <- 0.4^0.5
# sigma_prop <- matrix(c(0.138, -0.023, -0.023, 0.1), 2) * 2.38 ^ 2 / 2
sigma_prop <- 0.001 * diag(5)
disc_mat <- cbind(discrimination1, discrimination2)
L_a <- lower.tri(disc_mat, diag = TRUE) * 1
T_gp <- diag(m)

# RUN --------------------------------------------------------------------------

Rcpp::sourceCpp("../src/mirt-gibss-sp.cpp")
source("../R/ggplot-mcmc.R")
Rcpp::sourceCpp("../src/ifa-main.cpp")

# set.seed(5)
system.time(
  samples <- ifa_gibbs_sp(response, dist, n, q, m, cor.params, sig.params,
                          Corr[1:2, 1:2], fix.sigma, sigma_prop, L_a, T_gp, 0.234,
                          iter)
)
##    user  system elapsed 
##  40.405  23.996  16.568
# system.time(
#   samples <- spmirt(response = response, nobs = n, nitems = q, nfactors = 2,
#                     L_rest = L_a, niter = iter)
#   )

samples_tib <- as_tibble.spmirt.list(samples, iter/2)
summary(samples_tib)
## # A tibble: 3,634 x 6
##    Parameters `2.5%`   `10%`   `50%`  `90%` `97.5%`
##    <fct>       <dbl>   <dbl>   <dbl>  <dbl>   <dbl>
##  1 V1         -0.668 -0.436   0.278   1.10   1.41  
##  2 V2         -2.83  -2.39   -1.63   -0.941 -0.632 
##  3 V3         -0.621 -0.391   0.259   0.912  1.24  
##  4 V4          0.195  0.445   1.09    1.82   2.43  
##  5 V5         -1.25  -0.906  -0.245   0.365  0.683 
##  6 V6         -0.520 -0.0358  0.542   1.18   1.68  
##  7 V7         -0.717 -0.390   0.212   0.778  1.07  
##  8 V8         -1.86  -1.35   -0.724  -0.140  0.145 
##  9 V9         -2.26  -1.68   -0.882  -0.196  0.0795
## 10 V10        -1.08  -0.697   0.0152  0.595  0.958 
## # ... with 3,624 more rows
samples_long <- gather(samples_tib)

as_tibble.spmirt.list(samples, 0, 10, "c") %>%
  gg_trace(alpha = 0.6)

as_tibble.spmirt.list(samples, 0, 10, "a") %>%
  gg_trace(alpha = 0.6)

as_tibble.spmirt.list(samples, iter/2, 10, "a") %>%
  gg_density(alpha = 0.5, ridges = TRUE, aes(fill = Parameters), scale = 4)
## Picking joint bandwidth of 0.0967

as_tibble.spmirt.list(samples, iter/2, 10, "theta") %>%
  dplyr::select(1:100) %>%
  gg_density(alpha = 0.5, ridges = TRUE, aes(fill = Parameters), scale = 4)
## Picking joint bandwidth of 0.218

as_tibble.spmirt.list(samples, 0, 10, "theta") %>%
  select(1:10) %>%
  gg_trace(alpha = 0.6)

as_tibble.spmirt.list(samples, 0, 10, "mgp_sd") %>%
  gg_trace(alpha = 0.6)

as_tibble.spmirt.list(samples, 0, 10, "mgp_phi") %>%
  gg_trace(alpha = 0.6)

as_tibble.spmirt.list(samples, 0, 10, "a") %>%
  gg_density2d(`Discrimination 1`, `Discrimination 2`, each = 10,
               keys = c("Item ", "Discrimination "),
               highlight = c(discrimination1, discrimination2))
## Warning: Computation failed in `stat_density2d()`:
## bandwidths must be strictly positive

as_tibble.spmirt.list(samples, 0, 10, "a") %>%
  gg_scatter(`Discrimination 1`, `Discrimination 2`, each = 10,
               keys = c("Item ", "Discrimination "),
               highlight = c(discrimination1, discrimination2))

as_tibble.spmirt.list(samples, iter/ 2, select = "a") %>%
  summary() %>%
  mutate(param = c(discrimination1, discrimination2)) %>%
  gg_errorbarh() +
  geom_point(aes(param, Parameters), col = 3)

as_tibble.spmirt.list(samples, iter/2, select = "c") %>%
  summary() %>%
  mutate(param = as.numeric(difficulty)) %>%
  gg_errorbarh() +
  geom_point(aes(param, Parameters), col = 3)

as_tibble.spmirt.list(samples, iter/2, select = "theta") %>%
  dplyr::select(1:300) %>%
  summary() %>%
  mutate(param = data_geo$response[1:300]) %>%
  gg_errorbarh(sorted = TRUE) +
  geom_point(aes(x = param), col = 3)

as_tibble.spmirt.list(samples, iter/2, select = "theta") %>%
  dplyr::select(301:600) %>%
  summary() %>%
  mutate(param = data_geo$response[301:600]) %>%
  gg_errorbarh(sorted = TRUE) +
  geom_point(aes(x = param), col = 3)

ability1_pred <- as_tibble.spmirt.list(samples, iter/2, select = "theta") %>%
  dplyr::select(1:300) %>%
  summary() %>%
  mutate(param = data_geo$response[1:300],
         s1 = data_geo$s1[1:300],
         s2 = s1,
         estim = `50%`)
ability1_pred %>%
    ggplot(aes(s1, `50%`)) +
    geom_line() +
    geom_line(aes(s1, param, col = "real"))

vg <- gstat::variogram(estim ~ 1, ~ s1 + s2, ability1_pred, cutoff = 1, width = 0.01)
ggplot(vg, aes(dist, gamma)) +
  geom_point(aes(size = np)) +
  geom_smooth() +
  expand_limits(y = 0, x = 0) +
  scale_x_continuous(limits = c(0, 0.7))
## `geom_smooth()` using method = 'loess' and formula 'y ~ x'
## Warning: Removed 30 rows containing non-finite values (stat_smooth).
## Warning: Removed 30 rows containing missing values (geom_point).

ability2_pred <- as_tibble.spmirt.list(samples, iter/2, select = "theta") %>%
  dplyr::select(301:600) %>%
  summary() %>%
  mutate(param = data_geo$response[301:600],
         s1 = data_geo$s1[301:600],
         s2 = s1,
         estim = `50%`)
ability2_pred %>%
  ggplot(aes(s1, `50%`)) +
  geom_line() +
  geom_line(aes(s1, param, col = "real"))

vg <- gstat::variogram(estim ~ 1, ~ s1 + s2, ability2_pred, cutoff = 1, width = 0.005)
ggplot(vg, aes(dist, gamma)) +
  geom_point(aes(size = np)) +
  geom_smooth() +
  expand_limits(y = 0, x = 0) +
  scale_x_continuous(limits = c(0, 0.7))
## `geom_smooth()` using method = 'loess' and formula 'y ~ x'
## Warning: Removed 60 rows containing non-finite values (stat_smooth).
## Warning: Removed 60 rows containing missing values (geom_point).

# # # PREPARE DATA FOR MODELLING ---------------------------------------------------
# #
# # Y <- data_model %>% dplyr::select(id, response, response_label) %>%
# #   spread(response_label, response) %>%
# #   arrange(id) %>%
# #   dplyr::select(-id) %>%
# #   as.matrix()
# #
# # X <- data_model %>% dplyr::select(id, matches("^x[[:digit:]]+$")) %>%
# #   unique() %>%
# #   arrange(id) %>%
# #   dplyr::select(-id) %>%
# #   as.matrix()
# #
# # Beta <- matrix(beta, nrow = 1)
# # Sigma_proposal <- diag(1, 3)
# #
# # # RUN MODEL --------------------------------------------------------------------
# #
# # getwd()
# # Rcpp::sourceCpp("../src/multi-lm.cpp")
# # source("../R/ggplot-mcmc.R")
# #
# # iter <- 10^6
# # system.time(
# #   samples <- multi_lm(Y, X, iter, 0.01 * Sigma_proposal, 0.001 * Sigma_proposal)
# # )
# # samples %>% map(~ tail(.))
# #
# # # apply(samples$beta, 2, mean)
# # # cor(samples$beta)
# #
# # # Visualize traces
# # as_tibble(samples, 0, 100, select = "beta") %>%
# #   gg_trace(wrap = TRUE, alpha = 0.6)
# #
# # as_tibble(samples, 0, 100, select = "beta") %>% gg_trace(alpha = 0.6)
# # as_tibble(samples, 0, 100, select = "corr_chol") %>% gg_trace(alpha = 0.6)
# # as_tibble(samples, 0, 100, select = "corr") %>% gg_trace(alpha = 0.6)
# # as_tibble(samples, 0, 100, select = "sigmas") %>% gg_trace(alpha = 0.6)
# #
# # bla <- as_tibble(samples, iter/2, select = "sigmas")
# # cov(log(bla))
# # nrow(unique(bla)) / nrow(bla)
# #
# # bla <- as_tibble(samples, iter/2, select = "corr_chol")
# # cov(bla)
# # nrow(unique(bla)) / nrow(bla)
# #
# # # Visualize densities
# #
# # as_tibble(samples, iter / 2, select = "corr_chol") %>%
# #   gg_density(aes(fill = Parameters), scale = 2, alpha = 0.5, ridges = TRUE)
# #
# # as_tibble(samples, iter / 2, select = "corr") %>%
# #   gg_density(aes(fill = Parameters), scale = 1, alpha = 0.5, ridges = TRUE)
# #
# # # Visualize credible intervals
# # as_tibble(samples, iter / 2, select = "beta") %>%
# #   summary() %>%
# #   mutate(param = beta) %>%
# #   gg_errorbarh() +
# #   geom_point(aes(param, Parameters), col = 3)
# #
# # Corr_chol <- t(chol(Corr))
# # corr_chol <- Corr_chol[lower.tri(Corr_chol, diag = TRUE)]
# # corr <- Corr[lower.tri(Corr)]
# #
# # as_tibble(samples, iter / 2, select = "corr_chol") %>%
# #   summary() %>%
# #   mutate(param = corr_chol) %>%
# #   gg_errorbarh() +
# #   geom_point(aes(param, Parameters), col = 3)
# #
# # as_tibble(samples, iter / 2, select = "corr") %>%
# #   summary() %>%
# #   mutate(param = corr) %>%
# #   gg_errorbarh() +
# #   geom_point(aes(param, Parameters), col = 3)
# #
# #
# # as_tibble(samples, iter / 2 ,select = "sigmas") %>%
# #   summary() %>%
# #   mutate(param = sigmas) %>%
# #   gg_errorbarh() +
# #   geom_point(aes(param, Parameters), col = 3)
# #
# #
# # # Visualize credible intervals for all Parameters
# # as_tibble(samples, iter / 2) %>%
# #   summary() %>%
# #   mutate(param = c(beta, corr_chol, corr, sigmas)) %>%
# #   gg_errorbar() +
# #   geom_point(aes(Parameters, param), col = 3)
# #